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Item Detail

Defects in Liquid Crystals: Computer Simulations, Theory and Experiments

Author(s): Lavrentovich, Oleg D.; Pasini, Paolo; Zannoni, Claudio; Zumer, Slobodan; North Atlantic Treaty Organization. Scientific Affairs Division

ISBN10: 140200169X

ISBN13: 9781402001697

Cover: Hardcover

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Topological defects are the subject of intensive studies in many different branches of physics ranging from cosmology to liquid crystals and from elementary particles to colloids and biological systems. Liquid crystals are fascinating materials which present a great variety of these mathematical objects and can therefore be considered as an extremely useful laboratory for topological defects. This book is the first attempt to present together complementary approaches to the investigations of topological defects in liquid crystals using theory, experiments and computer simulations.

Provides an up to date coverage of issues and considers a number of outstanding open problems which can be tackled.

Preface

xiii

Classification of defects in liquid crystals

(16)

H.-R. Trebin

Introduction

(1)

Order and defects in a prototype model: the planar ferromagnet or the XY-model

(2)

Perfect order

(1)

The distorted ferromagnet

(1)

Singularities

(1)

Classification of defects

(4)

Testloops and winding numbers

(1)

Defect equivalence and stability

(2)

Defect processes and group structure

(1)

Further examples of reduced order parameter spaces and fundamental groups

(2)

Two-dimensional nematics

(1)

Two-dimensional smectics without rotations

(1)

Two-dimensional periodic crystals

(1)

Two-dimensional smectics with rotations

(1)

Singularities in three dimensions

(4)

Line singularities

(1)

The Three-dimensional ferromagnet (Heisenberg-model) and point singularities

(1)

Defects of three-dimensional nematics

(1)

Biaxial nematics and cholesteric liquid crystals

(1)

Homotopy classification of defects in three dimensions

(1)

Topological solitons

(2)

Planar and linear topological solitons

(1)

Periodic boundary conditions

(1)

Summary and conclusions

(1)

Alignment tensor versus director description in nematic liquid crystals

(20)

A.M. Sonnet

S. Hess

Introduction

(1)

Description of the Alignment

(9)

Distribution Function and Averages

(1)

Alignment Tensor

(8)

Dynamic equation for the alignment tensor

(4)

Director description

(1)

Tensor description

(3)

Examples

(6)

Visualization and s=1/2 disclination

(1)

Capillary

(1)

Droplet

(4)

Liquid crystal colloidal dispersions

(50)

H. Stark

A. Borstnik

S. Zumer

Introduction

(3)

Colloidal Dispersions in a Nematic Solvent

(22)

What is the Director Field?

(4)

One-Particle Properties

(9)

Two-Particle Interactions in a Nematic Solvent

(3)

Nematic Colloidal Dispersions in Complex Geometries

(6)

Colloidal Dispersions above the Nematic-Isotropic Phase Transition

(18)

Stability criteria for colloidal dispersions

(2)

Noncharged liquid crystal colloidal dispersions at temperatures above TNI

(10)

Charged spherical particles immersed in an isotropic liquid crystal

(6)

Conclusions

(7)

Computer simulations and defects in confined liquid crystal lattice models

(26)

C. Chiccoli

P. Pasini

I. Feruli

C. Zannoni

Introduction

(1)

Liquid Crystal Lattice Models

(3)

The Lebwohl-Lasher model

(1)

Monte Carlo simulations

(1)

Polymer Dispersed Liquid Crystals

(13)

Radial Boundary Conditions (RBC)

(12)

Nematic Films

104

(6)

Hybrid aligned cell

105

(4)

Schlieren textures in planar aligned cells

109

(1)

Conclusions

110

(3)

Molecular simulations and theory of planar interfaces and defects in nematic liquid crystals

113

(28)

M.P. Allen

Computer simulations and theoretical approaches

113

(3)

Simulation Models

113

(1)

Simulation Methods

114

(1)

Coarse-grained descriptions

114

(2)

Liquid crystals between parallel walls

116

(3)

Surface anchoring coefficient

116

(1)

Elastic boundary condition

117

(2)

Nematic-isotropic interface

119

(9)

Orientational order and density profiles

119

(1)

Results at high elongation

120

(2)

Surface Tension

122

(4)

Capillary waves

126

(2)

Disclination in cylindrical pores

128

(4)

Defects near a colloid particle

132

(5)

Saturn ring defect

133

(1)

Satellite defect

134

(3)

Off-center ring

137

(1)

Acknowledgements

138

(3)

Topological defect behavior in a quenched nematic liquid crystal

141

(26)

R.A. Pelcovits

J.L. Billeter

A.M. Smondyrev

G.B. Loriot

Introduction

142

(4)

Numerical simulations

146

(2)

Defect-finding algorithms

148

(4)

Results

152

(8)

Coarsening sequence

152

(2)

Real--space correlation function

154

(2)

Structure factor

156

(4)

Conclusions

160

(3)

Acknowledgements

163

(4)

Restoring forces on nematic disclinations

167

(18)

R. Rosso

E.G. Virga

Introduction

167

(2)

Restoring force and torque

169

(5)

Core's influence

174

(3)

Elliptic core

176

(1)

Director's moulding

177

(2)

Boundary's influence

179

(6)

Challenges in the dynamics of point defects

185

(16)

A.M. Sonnet

E.G. Virga

Introduction

185

(1)

Elastic force

186

(3)

Defect drift

189

(4)

Discretization of planar director fields

193

(2)

Artefacts in numerical defect dynamics

195

(6)

Numerical simulation of elastic anisotropy in nematic liquid crystalline polymers

201

(28)

H. Tu

G. Goldbeck-Wood

A.H. Windle

Introduction

202

(1)

Model

203

(3)

The calibration of the model

206

(5)

Reproducing the Freedericksz transitions

206

(2)

Topological defects in thin films

208

(1)

Coarsening of the defects

209

(2)

Disclinations in bulk samples

211

(4)

Twist type or wedge type

212

(2)

Escaped integer disclinations

214

(1)

Texture evolution under shear flow

215

(9)

Out--of--plane

219

(1)

Interaction of wedge disclination pairs under shear flow

220

(4)

Summary

224

(5)

Computer Simulations and Fluorescence Confocal Polarizing Microscopy of Structures in Cholesteric Liquid Crystals

229

(42)

S.V. Shiyanovskii

I.I. Smalyukh

O.D. Lavrentovich

Introduction

229

(2)

Mathematical basis for computer simulations of equilibrium LC structures

231

(4)

LC structure and elastic properties

231

(2)

Electric field

233

(1)

Surface anchoring

233

(2)

Domain and scheme of simulations

235

(1)

Confocal Microscopy and Fluorescence Confocal Microscopy

235

(8)

Confocal Microscopy

236

(1)

Fluorescence Confocal Microscopy

236

(2)

Fluorescence Confocal Polarizing Microscopy

238

(3)

Theoretical foundations of confocal microscopy of orientation patterns

241

(2)

Experimental set up and materials

243

(3)

Experimental set up

243

(1)

Liquid crystal materials and fluorescent probes

244

(2)

Results and Discussion

246

(14)

FCPM of Fredericks transition

246

(1)

FCPM of twisted nematic cell

247

(1)

The FCPM imaging of basic cholesteric textures

248

(4)

Field-induced cholesteric stripes in thin cells with planar boundary conditions

252

(5)

Cholesteric stripes in thin cells with homeotropic boundary conditions

257

(3)

Conclusions

260

(3)

Acknowledgements

263

(8)

Defects and Undulation in Layered Liquid Crystals

271

(30)

T. Ishikawa

O. D. Lavrentovich

Introduction

272

(1)

Bulk Elastic and Surface Properties of Lamellar Systems

273

(5)

Weakly distorted Smectic A phase in two dimensions

274

(1)

Lubensky-de Gennes coarse-grained model of the cholesteric phase

275

(2)

Surface Anchoring

277

(1)

Edge Dislocations

278

(8)

Linear Theory

279

(2)

Experimental Dislocation Profile and Non-linear Theory

281

(5)

Layers undulations (Helfrich-Hurault instability)

286

(12)

Helfrich-Hurault model

287

(2)

Undulations Profile near the Threshold: Experiment

289

(3)

Undulations in a Cell with a Finite Anchoring

292

(2)

Undulations profile well above the Threshold

294

(4)

Conclusion

298

(3)

Liquid crystals under shear: role of defects

301

(22)

M. Kleman

C. Meyer

Introduction

301

(2)

Disclinations

303

(3)

Generalities

303

(1)

Istabilities and defects in the LE regime

303

(1)

Instabilities and defects in the Doi regime (De ≫ 0.1)

304

(1)

Isolated disclination

305

(1)

Dislocations vs disclinations

306

(3)

Core structure and physical properties

309

(2)

Smectics

311

(12)

General relationships

311

(3)

Movement of isolated dislocations in a SmA phase

314

(3)

Collective behavior of dislocations: climb of edges

317

(2)

Collective behavior of dislocations: glide of screws

319

(1)

A Particular case of reorganization in smectic phases: the onion texture

320

(3)

Numerical simulation of defects in quasicrystals

323

(14)

H.-R. Trebin

Crystals and quasicrystals

323

(4)

Characteristic features of crystals and quasicrystals

323

(2)

Structure models for quasicrystals

325

(1)

Model quasicrystals

326

(1)

The cut formalism and phason-degree of freedom

327

(2)

The cut formalism

327

(1)

Phonon and phason degree of freedom

328

(1)

Dislocations in crystals and quasicrystals

329

(3)

Geometric basis

329

(1)

Experimental observations

330

(1)

Atomic interaction and numerical algorithm

331

(1)

Dislocation motion in the two-dimensional model

331

(1)

Dislocation motion in the three-dimensional model

332

(1)

Crack propagation

332

(3)

Summary and conclusion

335

(1)

Acknowledgement

336

(1)

Index

337

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